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THE 



METKIC SYSTEM 



OF 



WEIGHTS AND MEASURES 



BY 

*^ 

c- if * 

E. K SEAVER and G: A. : WALTON 



k^ 




BOSTON 
WILLIAM WARE AND COMPANY 

[Successors to Brewer and Tileston] 

1878 



PREFACE 



The following pages, taken mainly from the Franklin Written 
Arithmetic, are intended to present the Metric System of Weights 
and Measures in a simple and practical way, for the purposes of 
school instruction. 

This system has been presented by itself, unencumbered by com- 
parisons between its units and the units now in common use. Such 
comparisons are given at the end. This course is believed to be 
the best ; for pupils will form clear and lasting impressions of the 
meter, the liter, the gram, their multiples and subdivisions, not by 
being told how many inches, quarts, or grains they are equivalent 
to, but hy seeing and using the actual measures and weights until 
he becomes perfectly familiar with them. When a pupil knows 
the new measures well, he may then begin to make comparisons 
between the new measures and the old. 

A table of specific gravities has been added, with a few examples 
to illustrate its usefulness, especially when employed in connection 
with metric weights and measures. 



Copyright, 1S7S, 
By E. P. Seaver and G. A. Walton. 



K 



THE 



METRIC SYSTEM 



OF 



WEIGHTS AND MEASURES. 



§ 1. The metric system of weights and measures, now 
used in the greater part of Europe and coming into use 
in the United States, is derived from the standard meter. 

Note. The word meter means a measure. The standard meter is a 
certain bar of platinum carefully preserved at Paris. Copies of this bar, 
made with the utmost precision, have been procured and are carefully pre- 
served by the nations that have adopted the Metric System. The standard 
meter of the United States is such a copy, and it is kept at Washington. 
The meter-sticks made for ordinary use are copies of the standard meter. 



MEASURES OF LENGTH. 

§ 2. The standard unit of length in the metric system 

is the meter. 

Note. The teacher should show the pupil a meter and its subdivisions. 
If none can readily be obtained, a meter can easily be made from the decimeter 
represented on the next page. This meter may be divided into decimeters 
and centimeters. From this measure the pupils can easily make their own 
of paper or wood. 

§ 3. One tenth of a meter is a dec'i-meter. 

Note. The prefix deci- means one tenth of 

§ 4. One hundredth of a meter is a cenfti-meter. 

Note. The prefix centi- means one hundredth of 

§ 5. One thousandth of a meter is a mil'li-meter, 

Note. The prefix milli- means one thousandth of 



4 



THE METRIC SYSTEM. 



H 
W 

g 

o 
w 

p 

w 
ft 
O 



§ 6. Exercises on the Meter and its subdivisions. 

a. How many meters long is the room ? How many meters 
wide ? 

b. How many decimeters long is the 
table ? 

c. How many decimeters wide is the 
door ? 

d. How many centimeters long and wide 
is your slate ? the window-pane ? etc. 

e. How many millimeters apart are two 
lines on a sheet of writing-paper ? 

/. How many millimeters thick is your 
slate-frame ? your ruler ? etc. 

g. How many millimeters are there in one 
centimeter ? 

h. How many centimeters are there in one 

decimeter ? 

i. How many decimeters are there in one 
meter? 

j. How many millimeters are there in one 
decimeter ? in one meter ? 

k. How many centimeters are there in 
37 millimeters, and how many millimeters 
remain ? 

1. How many decimeters are there in 84 
centimeters, and how many centimeters re- 
main ? 

in. How many meters are there in 347 centimeters, and how 
many centimeters remain ? 

22. In measuring the length of the room, did you find it to 
he an exact number of meters long ? 

o. If not, how many decimeters do you find in the remain- 
der ? Do you find an exact number of decimeters ? 

p. If there is still a remainder, how many centimeters do 
you find in it ? 



MEASURES OF LENGTH. O 

To write Numbers in the Metric System. 

§ 7. To express a length in meters and parts of a 
meter, we write whole meters in the units' place, deci- 
meters in the tenths' place, centimeters in the hundredths' 
place, and millimeters in the thousandths' place. 

Thus, if a room is found to be 8 meters 6 decimeters 
9 centimeters long, we write : 

Length of the room == 8.69 meters. 

2 decimeters 3 centimeters 5 millimeters is written : 

0.235 meters. 

§ 8, The abbreviations used in writing expressions of 
length are : For meters, m ; for decimeters, dm \ for centi- 
meters, cm ; and for millimeters, mm. 

§ 9. Lengths may be expressed in other denominations 
as well as in meters, by putting the decimal point at the 
right of the place of the required denomination y and writing 
the proper name or abbreviation after the figures. 

Thus, 0.235 m may be written 2.35 dm , 23.5 cm , or 235 mm . 
So also 728 mm may be written 72.8 cm ? 7.28 dm , or 0.728 m . 

§ 10. Exercises in reading Numbers. 

Read the following : 



a. 5 m 


e. 5.926 m 


L 6.58 dm 


b. 47 m 


/. 36 dm 


j, 3.4 cm 


c. 3.9 m 


g. 428 cm 


k. 43.7 cm 


d. 4.21 m 


h. 23 mm 


1. 2.5 mm 



§ 11. Examples for the Slate. 

Change the following to meters : 

(1.) l dm (4.) l cm (7.) l mra 

(2.) 13 dm (5.) 38 cm (8.) 48 ram 

(3.) 214 dm (6.) 529 cm (9.) 3675 



6 THE METRIC SYSTEM. 

Multiples of the Meter. 

§ 12. Besides the meter and its subdivisions, there are 
longer measures, which are multiples of the meter. 

§ 13. The dek'a-meter is ten times as long as the meter. 
Note. The prefix deka- means tenfold. 

§ 14. The hek'to-meter is a hundred times as long as 
the meter. 

Note. The prefix hekto- means a hundredfold. 

§ 15. The kiTo- meter is a thousand times as long as 
the meter. 

Note. The prefix kilo- means a thousandfold. 

§ 16. The my'ria-meter is ten thousand times as long 

as the meter. 

Note. The prefix myria- means ten thousandfold. 

Note. Of these longer measures, the kilometer is used in measuring 
distances on roads, canals, rivers, etc. The other measures are much less 
frequently used ; the myriameter hardly ever. 

§ 17. Exercises on the Multiples of the Meter. 

a. Measure off a string ten meters long. What name is 
given to the length of this string? 

Note. The string may be used in measuring distances. For this pur- 
pose it will be well to make knots at the end of each meter. 

b. Measure in dekameters and meters the length and 
breadth of the school-yard; of a garden; of a field, etc. 

c. Measure off in the street, or other convenient place, a 
distance of 10 dekameters. What name is given to this distance? 

d. Walk from the beginning to the end of the distance thus 
measured off, and count your paces. How many of your paces 
make a hektometer ? 

e. How many of your paces would make a kilometer ? 

/. How many kilometers from your home to the school-house? 



MEASURES OF LENGTH. I 

g. How long does it take you to walk a kilometer ? 
h. How many kilometers can you walk in an hour ? 
i. If 1500 of your paces make a kilometer, how many make 
a dekameter ? 

§ 18. To express distances in meters and multiples of a 
meter, we write meters in the units' place, dekameters in 
the tens' place, hektometers in the hundreds' place, and so on. 

§ 19. To express a distance in kilometers, we write 
kilometers in the units' place, and then hektometers, 
dekameters, and meters will be written in the tenths', hun- 
dredths', and thousandths' places respectively. 

Thus, if the distance from one town to another is found 
to be 9780 meters, the usual form of writing would be 
9.78 kilometers. 

Note. The greatest distances are usually expressed in kilometers. Thus, 
the distance of the earth from the sun is about 149000000 kilometers. 

§ 20. The abbreviations used in writing are : For the 
dekameter, Dm ; for the hektometer, Hm ; and for the 
kilometer Km. 

§ 21. Table of Long Measure. 
10 millimeters (mm) = 1 centimeter (cm). 
10 centimeters = 1 decimeter (dm). 

10 decimeters = 1 meter (m). 

10 meters = 1 dekameter (Dm). 

10 dekameters = 1 hektometer (Hm). 

10 hektometers — 1 kilometer (Km). 

10 kilometers = 1 myriameter (Mm). 

§ 22. Oral Exercises. 

Read the following : 

a. 123 m d. 42 Dm g. 49 Km 

b. 497.6 m e. 36.7 Dm h. 593.7 Km 

c. 346 Hm /. 57.5 Hra I 6000 Kra 



8 



THE METRIC SYSTEM. 

§ 23. Examples for the Slate. 

Change the following to meters : 

(10.) 425 Dm (13.) 94.6 Hm (16.) 0.72 Kra 

(11.) 35 Hm (14.) 9.24 Km (17.) 0.073" 

(12.) 23.5 Km (15.) 39.7 Dm (18.) 0.05 



Km 



Addition, Subtraction, Multiplication, and Division of Metric 

Numbers. 

§ 24. Illustrative Example. Change to meters and 
add 14.83 Dm , 75.6 Hm , and 948 cm . 

written work. Explanation. — When these expressions 

14.83 Dm = 148.3 m have been changed to meters, they are all 

75.6 Hm = 7560. of the same denomination, and the sum is 

948 cm = 9.48 found in the same way as in the addition 

7717 78 m °^ s i m pl e numbers. 

§ 25. Numbers expressing metric measures and weights 
are added, subtracted, multiplied, and divided by the same 
rules as apply to simple numbers. 

§ 26. Examples for the Slate. 

19. Add 5.6 m ? 24.07 m , 30.5 m , and 7.508 m . 

20. Express as meters and add 582 cm , 6428 dm , and 495 mm . 

21. Express as meters and add 369 Dm , 4073 Hm , and 5 Km . 

22. Add 48.06 m , 709.63 ra ; 3708.9 m , 800.9 m , and express the 
answer in kilometers. 

23. If 7 Km be taken from 42 Km ; how many meters remain ? 

24. From 87.04 m take 42 cm . 

25. The distance round a certain park is 2.58 kilometers. 
How many meters will a man go who rides around it six times ? 

26. A school-boy walked one third around the above park in 
12 minutes. How many meters did he walk in 1 minute ? 

27. How many kilometers in 36.68 m x 2004 ? 

28. Divide 38.07 m by 4 and by 3, and add the answers. 

29. Ellen's hoop is 3.6 m around. How many times will it 
turn in rolling a distance of 1.08 Km ? 



MEASURES OF SURFACE. 9 

MEASURES OF SURFACE. 

§ 27. The units used in measuring surfaces are squares, 
each having sides equal to a unit of long measure. 

Thus, a square meter is a square having sides one meter 
long; a square decimeter is a square having sides one 
decimeter long ; etc. 

§ 28. Exercises. 

a. How many square decimeters in a square meter ? Illus- 
trate by drawing a square meter on the blackboard or on the 
floor and dividing it into square decimeters. 

b. How many square centimeters in a square decimeter ? 
Illustrate by drawing a square decimeter on your slate and 
dividing it into square centimeters. 

c. How many square meters in a square dekameter ? 

§ 29. The square dekameter, when used as a unit of 
land measure, takes a special name, and is called an ar. 
One hundredth of an ar, which is one square meter, is 
called a centar. A hundred ars, equal to one square 
hektometer, is called a hektar. 

§ 30. Square Measure. 

100 square millimeters (sq mm) = 1 square centimeter (sq cm). 

100 square centimeters = 1 square decimeter (sq dm). 

100 square decimeters = 1 square meter (sq m) ' = 1 centar (ca). 

100 square meters = 1 square dekameter = 1 ar (a). 

100 square dekameters = 1 square hektometer = 1 hektar (Ha). 

100 square hektometers — 1 square kilometer (sq Km). 

§ 31. As the units of square measure form a scale of 
hundreds, in writing numbers expressing surface two deci- 
mal places must be allowed for each denomination. 

Thus, 45 sqra 4 sqdm 86 sqcm are written 45.0486 sqm ; and 7 Ha 
6 a 5 ca are written 706.05 a . 



10 



THE METRIC SYSTEM. 



§ 32. Examples for the Slate. 

30. How many square meters of carpeting will be required 
to carpet a room 5.3 m long and 4.5 m wide ? 

31. How many meters of carpeting 0.7 m wide will be re- 
quired to carpet a room 4 m long and 3.5 m wide ? 

32. What is the cost of polishing the surface of a rectangu- 
lar piece of marble 2.8 meters long and 1.2 meters wide, at 
8 2.50 per sq. meter ? 

33. In a piece of land 15 m long and 14.5 m wide are how 
many square meters or centars ? how many ars ? 

34. Express the following in ars and add them : 1.3 hektars, 
155.5 ars, 43 hektars, 26 centars. 

35. A had 6 hektars, 7 ars, 9 centars of land, and sold 0.2 of 
it at $ 54 an ar. How much did he receive for what he sold ? 



MEASURES OF VOLUME. 

§ 33. The units used in measuring cubic contents, or 
volume, are cubes, each having its edges equal to a unit 
of long measure. 

Thus, the cubic meter is a cube having edges one meter 
long; a cubic decimeter is a cube having its edges one 
decimeter long ; etc. 

§ 34. Exercises. 

a. How many cubic decimeters in a cubic meter ? 

b. How many cubic centimeters in a cubic decimeter ? 
Illustrate by means of a cubical block having edges one deci- 
meter long, marked off into centimeters. 

§ 35. The cubic meter, when used as a unit of measure 
for wood and stone, takes a special name, and is called a 
ster. 

§ 36. The cubic decimeter, when used as a unit of liquid 
or dry measure, is called a liter. 



MEASURES OF VOLUME. 11 

§ 37. Cubic Measure. 

1000 cubic millimeters (cu mm) = 1 cubic centimeter (cu cm). 

1000 cubic centimeters = 1 cubic decimeter (cu dm) = 1 liter. 

1000 cubic decimeters = 1 cubic meter (cu m) =1 ster. 

§ 38. Wood Measure. 

10 decisters (ds) = 1 ster (s). 

10 sters = 1 dekaster (Ds). 

§ 39. As the units of cubic measure form a scale of 
thousands, in writing numbers expressing volume three 
decimal places must be allowed for each denomination. 

Thus, 427 cu m 29 cu dm 3 cu cm are written 427.029003 cu m . 

§ 40. As the units of wood measure form a scale of tens, 
only one decimal place is needed for each denomination. 
Thus, 7 dekaster s 5 sters 6 decisters are written 75.6 sters. 

§ 41. Examples for the Slate. 

36. Express the following in cubic meters and add them : 
7 cu. meters 40 cu. decimeters ; 5 cu. meters 3 cu. decimeters 
19 cu. centimeters ; 25 cu. centimeters 49 cu. millimeters. 

37. How many cubic meters of earth must be removed to 
dig a cellar 14.5 ra long, 4.6 m wide, and 2.3 m deep ? 

38. At $ 1.25 a cubic meter, what will it cost to dig a trench 
75.5 m long, 2.2 m wide, and 1.8 m deep ? 

39. How many loads of earth, each filling 2.25 cu m , will fill 
a space 15.4 m long, 12 m wide, and 4.5 m deep ? 

40. If a cubic centimeter of gold is worth $12.50, what is 
the value of a brick of gold 2.4 cm long, 1.3 cm wide, and 0.75 cm 
thick ? 

41. If I burn 27 sters of wood in the three winter months, 
what must be the length of a pile 1 meter wide and § meter 
high to last a month, and what will it cost at % 2.25 a ster ? 



12 TEE METRIC SYSTEM. 

MEASURES OF CAPACITY. 

§ 42. The primary unit of measure for all substances 
that can be poured into a dish or box is the liter. 
§ 43. A liter is equal in volume to one cubic decimeter. 

§ 44. Larger and smaller measures are derived from the 
liter in the same way that longer and shorter measures 
are derived from the meter, that is, by taking decimal 
multiples and subdivisions. 

§ 45. Liquid and Dry Measures. 

1 milliliter (ml) = 1 cu cm. 

10 milliliters = 1 centiliter (cl). 

10 centiliters = 1 deciliter (dl). 

10 deciliters = 1 liter (1) = 1 cu dm. 

10 liters = 1 dekaliter (Dl). 

10 dekaliters = 1 hektoliter (HI). 

10 hektoliters = 1 kiloliter (Kl). = 1 cu m. 

Note. The milliliter is employed in computations, but rarely, if ever, 
in actual measurements. Chemists and druggists use cubic centimeters 
instead of milliliters. 

§ 46. Examples for the Slate. 

42. If one hektoliter of kerosene costs $20, what is the 
price of a liter ? 

43. What must be paid for 2.5 liters of milk each day for a 
week, at 7 cents a liter ? 

44. From a vessel containing 1 hektoliter of syrup, 25 liters 
were drawn out. How many liters remained ? 

45. How many hektoliters of oats can be put into a bin that 
is 2 m long, 1.3 m wide, and 1.5 m deep? 

46. What must be the length of a bin 1 meter wide and 
1 meter deep, to contain 4500 liters of grain ? 



WEIGHTS. 13 

WEIGHTS. 

§ 47. The primary unit of weight is the gram. 

§ 48. A gram is the weight of one cubic centimeter 
of pure water at the temperature of 4 degrees centigrade 
(=39.2 degrees Fahrenheit), at which temperature water 
has its greatest density. 

§ 49. Larger and smaller weights are derived from the 
gram by taking decimal multiples and subdivisions. 

§ 50. Weights. 
10 milligrams (mg) = 1 centigram (eg). 
10 centigrams = 1 decigram (dg). 

10 decigrams = 1 gram (g) — wt. of 1 cu cm of water. 

10 grams = 1 dekagram (Dg). 

10 dekagrams = 1 hektogram (Hg). 

10 hektograms = 1 kilogram (K) = wt. of 1 cu dm of water. 
10 kilograms = 1 myriagram (Mg). 

10 myriagrams = 1 quintal (Q). 
10 quintals = 1 metric ton (T.) = wt. of 1 cu m of water. 

Note I. The gram, kilogram, and metric ton are the only units used in 
actual weighing, except by jewellers, druggists, and those who weigh very 
small or very expensive articles, like gold or powerful medicines. 

Note II. The kilogram is generally called the kilo. The kilo is the 
unit of weight for weighing common articles, such as sugar, tea, etc. 

Note III. The metric ton is used to weigh very heavy articles, like 
hay, coal, etc. 

§ 51. Examples for the Slate. 

47. At $ 0.60 a kilo for honey, what is the cost of 5.15 kilos ? 

48. At $ 11 per T. for coal, what will the coal cost to keep 
a fire one week if 30 kilos are burnt each day ? 

49. What weight of mercury will a vessel contain whose 
capacity is 10 cu cm ; mercury being 13.5 times as heavy as water ? 

50. If marble is 2.7 times as heavy as water, what is the weight 
of a pedestal 1 meter square at each end and 2 meters high ? 



14 



THE METRIC SYSTEM. 



§ 52. Table of Equivalents. 

The equivalents here given agree with those that have been established 
by Act of Congress for use in legal proceedings and in the interpretation of 
contracts. 



1 inch = 2. 540 centimeters. 
1 foot = 3.048 decimeters. 
1 yard = 0.9144 meters. 
1 rod = 0.5029 dekameters. 
1 mile = 1.6093 kilometers. 



1 centimeter = 0.3937 inch. 
1 decimeter = 0.328 foot. 
1 meter = 1.0936 yds. = 39.37 in. 
1 dekameter = 1.9884 rods. 
1 kilometer = 0.62137 mile. 



1 sq. inch = 6.452 sq. centimeters. 1 sq. centimeter = 0.1550 sq. inch. 
1 sq. foot = 9.2903 sq. decimeters. 1 sq. decimeter = 0.1076 sq. foot. 
1 sq. yard = 0.8361 sq. meter. 1 sq. meter = 1.196 sq. yards. 

1 sq. rod = 25.293 sq. meters. 1 ar = 3.954 sq. rods. 

1 acre = 0.4047 hektar. 1 hektar = 2.471 acres. 

1 sq. mile = 2.590 sq. kilometers. 1 sq. kilometer = 0.3861 sq. mile. 
1 cu.inch = 16.387 cu. centimeters. 1 cu. centimeter = 0.0610 cu. inch. 
1 cu. foot = 28.317 cu. decimeters. 1 cu. decimeter = 0.0353 cu. foot. 
1 cu. yard = 0.7645 cu. meter. 1 cu, meter = 1.308 cu. yards. 



1 cord = 3.624 sters. 
1 liquid quart = 0.9463 liter. 
1 gallon = 0.3785 dekaliters. 
1 dry quart = 1.101 liters. 
1 peck = 0.881 dekaliter. 
1 bushel = 3.524 dekaliters. 
1 ounce av. = 28.35 grams. 
1 pound av. = 0.4536 kilogram. 



1 ster = 0.2759 cord. 
1 liter = 1.0567 liquid quarts. 
1 dekaliter = 2.6417 gallons. 
1 liter = 0.908 dry quart. 
1 dekaliter = 1.135 pecks. 
1 hektoliter = 2.8375 bushels. 
1 gram = 0.03527 ounce av. 
1 kilogram = 2.2046 pounds av. 



1 ton (2000 lbs.) = 0.9072 met. ton. 1 metric ton = 1.1023 tons. 
1 grain Troy = 0.0648 gram. 1 gram = 15.432 grains Troy. 

1 ounce Troy = 31.1035 grams. 1 gram = 0.03215 ounce Troy. 
1 pound Troy = 0.3732 kilogram. 1 kilogram = 2.679 pounds Troy. 



EQUIVALENTS. 15 

§ 53. To change numbers in the metric system to equiva- 
lents of the old system : 

Examples. 

51. In 48 meters how many feet ? 

52. If you travel 50 kilometers in a day, how many miles 
do you travel ? 

53. Change 18 hektars of land to acres. 

54. How many inches long is an insect that is 5.2 centi- 
meters long ? 

55. How many pounds av. are there in 85.6 kilos of salt ? 

56. How many gallons are there in 24 kiloliters ? 

57. In 20 metric tons how many tons ? 

§ 54. To change numbers in the old system to equiva- 
lents of the metric system : 

Examples. 

58. Change 25 miles to kilometers. 

59. In 200 acres are how many hektars ? 

60. How many liters will a cistern hold that measures on the 
inside 5 feet in length, 4 feet in width, and 4 feet in height ? 

61. In 3 rods how many meters ? 

62. Change 18 qt. 1 pt. to liters. 

63. In 1 lb. 7 oz. 18 pwt. of gold, how many grams ? 

64. What is the weight of a barrel of flour (196 lbs.) in 
kilograms ? 

§ 55. Approximate Equivalents. 

The equivalents here given are accurate enough for most purposes, and 
are easy to remember. 



A meter 



A decimeter = 4 inches. 

3 ft. 3f in., 
or Ito yards. 

A dekameter = 2 rods. 

A kilometer = § of a mile. 

. (4 sq. rods, 

An ar = { , - 

( or - 4 x o of an acre. 

A hektar = 2J acres. 



A ster = J of a cord. 

1.06 liquid qt., 



A liter q « 

or -ft- of a dry qt. 

A dekaliter = 1 peck and 1 qt. 

A hektoliter == 2$ bushels. 

A gram = 15 \ grains. 

A kilogram = 2b pounds av. 

A metric ton = 2200 pounds av. 



16 THE METRIC SYSTEM. 

56. Miscellaneous Examples. 

65. A stage-coach is driven a distance of 70 Km in 8 hours. 
What is the rate per . hour ? 

66. A horse trotted a distance of 9.6 Km in 40 minutes. 
How far would he trot in an hour and a half at the same rate ? 

67. The distance from Boston to Albany is 325 Km . What 
is the rate of a railway-train that runs this distance in 8 hours 
and 20 minutes ? 

68. In walking from his home to the school-house a boy 
finds that he has taken 2468 paces. If four of his paces are 
equal to three meters, how many kilometers has he walked ? 
What is the length of a pace in centimeters ? 

69. How many kilometers will a man walk in 9^ hours if 
he walks at the rate of 5 kilometers an hour ? 

70. The distance from either pole to the equator is about 
ten million meters. How many days and hours would it take 
a railway-train running at the rate of 50 Km an hour to run 
around the world ? 

71. In 324560 hektars of land there are how many square 
kilometers ? 

72. What is the cost of a rectangular house-lot 58 m long 
and 48 m wide at $ 90 an ar ? 

73. A rectangular field 24 Dm long and 18 Dm wide produces 
hay at the rate of 75 K to the ar. What is the value of the 
whole crop at $ 23 a metric ton ? 

74. How many meters of lining that is 65 cm wide are needed 
to line 13 meters of silk that is 84 cm wide ? 

75. What is the cost of carpet for a room 10.5"^ long and 
8.4 m wide, if the carpet is 84 cm wide and costs $ 3.50 a meter ? 

76. A speculator bought 252 hektars of land at $325 a 
hektar, and sold § of it for house-lots at an average price of 
13 cents a square meter. Suppose that £ of the land is taken 
up by streets and lanes, and that the land still unsold is worth 
twice its original cost, what is the amount of gain on the in- 
vestment ? 



MISCELLANEOUS EXAMPLES. 17 

77. Express 63 cubic centimeters in decimals of a liter ? 

78. What part of a cubic meter is filled by 62^ dekaliters ? 
by 375 liters ? 

79. How many bricks, each 20 cm long, 10 cm wide, and 6 cm 
thick are needed to build a wall 30 m long, 1.8 m high, and 40 cm 
thick ? 

80. At $2.75 a ster, what is the value of a load of wood 
2 m long, 1.2 m wide, and 1.65 ra high ? 

81. How many sters of wood may be piled in a wood-shed 
7.5 m long, 4.8 m wide, and 4.2 m high ? 

82. How many double dekaliters full of grain will fill a bin 
2 m long, 1 m wide, and 80 cm deep ? 

S3. A bin is 2 m long and 1.15 m wide. How deep must it 
be to contain 20 hektoliters of grain ? 

84. A grocer bought 5 hogsheads of molasses, which, when 
gauged, measured in hektoliters as follows : 2.156, 2.271, 2.198, 
2.174, and 2.181. The whole cost $98.82. At what price a 
liter must the molasses be sold that there may be a gain of 
33i % ? 

85. I bought four loads of hay, which weighed 1.625, 1.843, 
1.970, and 1.758 metric tons respectively ? How many days 
will this hay last 5 horses if each horse is allowed 18 kilograms 
a day? 

86. A dray is loaded with 48 bags of grain, each bag hold- 
ing 8 dekaliters. What is the weight of the load in metric 
tons, allowing 75 kilos of grain to the hektoliter ? 

87. An arc of one degree on the equator measures 111.3066 
kilometers. What is the circumference of the earth at the 
equator in kilometers ? 

88. How many bottles each holding half a liter can be filled 
from a cask containing 1 hektoliter of wine ? 

89. At 8f a liter, what is the cost of supplying a family 
with 1.5 liters of milk daily through the three summer months ? 

90. A vender bought a hektoliter of peanuts for $ 11, and 
sold them at 20 cents a liter. How much did he gain ? 



18 THE ME TRIO SYSTEM. 

91. At $2.80 a hektoliter, what is the value of the corn 
raised on 5.76 hektars of land, the yield being at the rate of 
8.3 dekaliters an ar ? 

92. Express the weight of 364 cubic centimeters of pure 
water in decimals of a kilogram. 

93. What part of a kilogram of water will fill a centiliter ? 
How many kilograms of water will fill a cask holding a hekto- 
liter ? 

94. What is the capacity in liters of a jar that weighs 5.3 K 
when empty and 37.8 K when full of water ? 

95. What is the capacity in dekaliters of a cask that weighs 
23.7 K when empty and 129.8 K when full of water ? 

96. The depth of water in a flume is 8 meters. What is 
the pressure in kilograms on every square decimeter of the 
bottom ? 

97. A liter of dry air weighs 1.293 grams when the ther- 
mometer indicates a freezing temperature and the mercury in 
the barometer stands at the ordinary height (76 cm or 30 inches). 
What is the weight of the air in a room 10 m long, 9.5 m wide, 
and 4.6 m high, supposing the temperature and pressure to be 
as above stated ? 

98. What is the area of Massachusetts in square kilometers, 
its area in square miles being 7800 ? 

99. What price a liquid quart is equivalent to 15 f a liter ? 

100. The silver dollar weighs 4121 grains Troy. How many 
grams does it weigh ? 

101. What price a peck is equivalent to 80,^ a dekaliter ? 

102. What price a gram is equivalent to 62/ an ounce Troy ? 

103. A yield of 40 bushels of rye to the acre is equivalent 
to how many hektoliters to the hektar ? 

104. If a field produces 60 hektoliters of corn to the hektar, 
how many bushels is that to the acre ? 

105. A bushel of wheat weighs 60 pounds. What is the 
weight of a hektoliter of wheat in kilograms ? 

106. The pressure of the atmosphere is about 15 pounds to 



MISCELLANEOUS EXAMPLES. 19 

the square inch. What is that in kilograms to the square 
decimeter ? 

107. A " horse-power " is the amount of work that would he 
required to lift 33000 pounds one foot high in one minute; 
which is expressed briefly by saying that 1 horse-power equals 
33000 foot-pounds per minute. What is the value of 1 horse- 
power in kilogram-meters per minute ? 

108. A rectangular lot of land is § as wide as it is long, and 
contains 1944 ars. What is the cost of fencing the land if the 
fence costs 80 f a meter ? 

109. A ladder 15 meters long if placed at a certain point in 
a street will just reach a window 12 meters above the street on 
one side, or a window 9 meters above the street on the oppo- 
site side. How wide is the street ? 

110. A barn is 14.4 m wide, and the ridge-pole is 5.4 m higher 
than the eaves. How long are the rafters ? If the barn is 50 m 
long and 7.5 m high to the eaves, how many square meters of 
boards will be needed to board up the four sides and the roof ? 

111. Find the area of a triangle whose base is 1.37 m , and 
whose height is 1.24 m . 

112. The three sides of a triangle measure 50 m , 42 m , and 
36 m respectively. What is its area ? 

113. The four sides of a field measure 421 m , 367 m , 482 m , 
402 m respectively, and the diagonal connecting the ends of the 
two sides first mentioned measures 504 m . What is the area 
of the field in ars ? 

114. The two parallel sides of a trapezoid measure 2.53 m 
and 3.75 m respectively, and the distance between them is 
1.54 m . What is the area of the figure? 

115. What is the number of square decimeters in a board 
4.3 m long, 45 cm wide at one end, and 33 cm at the other ? 

116. What is the diameter of a tree if the girth is 3.78 m ? 
Note. In examples that require it, the ratio of the circumference to 

the diameter of a circle is taken to be 3y, unless otherwise stated. 

117. What must be the length of a horse's tether that he 
may be able to graze over just one ar of land ? 



20 THE METRIC SYSTEM. 

118. What are the dimensions of the largest square stick of 
timber that can be sawed out of a log that measures 1.89 m in 
girth ? 

119. A circular park 3.5 dekameters in diameter covers how 
many ars of land ? 

120. What is the capacity in cubic meters of a cylindrical 
tank 2.8 meters deep and 3 meters in diameter ? 

121. What is the capacity in liters of an ash-can 42 cm in 
diameter and 72 cm deep ? 

122. A cylindrical vessel is 49 cm in diameter. How deep 
must it be to hold 124 K of water ? 

123. What is the capacity in liters of a common water-pail 
which measures 28 cm in diameter at the top, 22 cm in diameter 
at the bottom, and 21 cm in depth ? 

Measures for grain are made of wood in cylindrical form, 
with depth and diameter equal. Taking the ratio of the cir- 
cumference to the diameter of a circle to be 3.1416, compute 
in millimeters the dimensions of the following measures, which 
are the ones commonly used : 

(124.) Hektoliter. (130.) Liter. 

(125.) Demi-hektoliter. (131.) Demi-liter. 

(126.) Double dekaliter. (132.) Double deciliter. 

(127.) Dekaliter. (133.) Deciliter. 

(128.) Demi-dekaliter. (134.) Demi-deciliter. 

' (129.) Double liter. 

Larger measures for liquids are made of copper or tin in the 
form above described ; but the smaller measures are made in 
cylindrical form, with a depth double the diameter. Compute 
in millimeters the dimensions of the following measures, made 
in the form last described : 

(135.) Double liter. (139.) Deciliter. 

(136.) Liter. (140.) Demi-deciliter. 

(137.) Demi-liter. (141.) Double centiliter. 

(138.) Double deciliter. (142.) Centiliter. 



SPECIFIC GRAVITY. 



21 



SPECIFIC GRAVITY. 

57. The specific gravity of a substance is the quotient 
obtained by dividing the weight of a given volume of the 
substance by the weight of an equal volume of water. 

58. This quotient has been ascertained by experiment 
for a great variety of substances, and some of the more 
useful results are given in the following 



Table of Specific Gravities. 



Alcohol, absolute... 0.795 

Ash-wood 0.845 

Beech- wood 0.852 

Brass, cast 7820 

Brass, sheet 8.390 

Brick 2.000 

Chestnut-wood 0.565 

Copper, hammered 8.900 

Cork 0.240 

Diamond 3.530 

Ether, sulphuric 0.715 

Ebony 1.331 

Glass, flint 3.000 

Glass, crown 2.520 

Gold, hammered 19.350 

Granite 2.65 to 2.75 

Ice 0.918 

Iron, cast 7.250 

Iron, wrought 7.780 

Lead, cast 11.350 

Lignum Vitae 1.333 

Limestone 2.60 to 2.70 

Mahogany- wood 1.063 



Maple-wood 0.790 

Marble 2.65 to 2.75 

Mercury 13.596 

Milk 1.031 

Muriatic acid 1.200 

Naphtha 0.840 

Nitric acid 1.500 

Oak, green 1.113 

Oak, seasoned 0.743 

Olive oH 0.915 

Pine- wood, hard 0.657 

Pine- wood, white 0.551 

Platinum, hammered 22.060 

Proof spirit 0.920 

Sandstone ....2.25 to 2.65 

Sea- water 1.025 

Silver, hammered 10.510 

Steel, soft.. 7.830 

Steel, tempered 7.810 

Sulphuric acid.. 1.841 

Tin, cast 7.290 

Wax 0.960 

Zinc 7.190 



22 THE METRIC SYSTEM. 

59. Since a cubic centimeter of pure water weighs 
1 gram, a cubic decimeter 1 kilogram, and a cubic meter 
1 metric ton, the numbers in a table of specific gravities 
show 

(1) the weight in grams of one cubic centimeter "" 

(2) the weight in kilograms of one cubic deci- . of any given 

meter (one liter) j substance. 

(3) the weight in metric tons of one cubic meter , 

60. From the above statement may be deduced the fol- 
lowing 

Rules. 

1. To find the weight of a substance when its volume is 
known : Multiply the volume by the specific gravity. 

2. To find the volume of a given substance when its 
weight is known : Divide the wcicjht by the specific gravity. 

61. Examples. 

143. What is the weight in kilograms of a cubical piece of 
cast-iron measuring 12 cm each w T ay ? 

144. What is the weight in kilograms of a cannon-ball of 
cast-iron 17.5 cm in diameter ? 

145. What is the diameter of a lead bullet of spherical 
shape weighing 14 grams ? 

146. What is the weight of a load of bricks, the number 
of bricks being 1000, and the dimensions of each 19 cm long, 
8.7 cm wide, and 6 cm thick? 

147. The front wall of a warehouse extending 15 m along the 
street is of granite, and is supported on iron columns. Find 
the pressure in metric tons on these columns, supposing the 
walls to be on the average 50 cm thick and to rise 12.5 m above 
the columns, and making no allowance for windows. 

148. A bottle weighing 254 grams when empty holds 



EXAMPLES, 23 

1.34 liters. What will it weigh when filled with sulphuric 
acid? 

149. A bottle weighs 803 grams when rilled with sulphuric 
ether and 241 grams when empty. What is the capacity of 
the bottle in liters ? 

150. What is the weight in kilograms of a maple plank 
4.3 m long, 63 cra wide, and 7.9 cm thick ? 

151. How many cubic centimeters of water would be dis- 
placed by a cubic decimeter of white-pine wood floating in it ? 
What fraction of the block would remain above water ? 

Note. A solid body floating in a liquid sinks far enough to displace its 
own weight of the liquid. 

152. What part of an iceberg floating in the ocean would be 
under water ? 

153. A bar of wrought-iron floats in mercury. What part 
of it is below the surface of the mercury ? 

154. A solid floating in water is J below water. What is 
the specific gravity of the solid ? 

155. A bottle holding just 750 cubic centimeters, and 
weighing when empty 157 grams, is filled with a certain liquid 
and is then found to weigh 976.5 grams. Find the specific 
gravity of the liquid. 

156. Wishing to ascertain the specific gravity of a piece of 
metal weighing 1432 grams, I sink it in a vessel that is just 
full of water and take it out again. Before this was done the 
vessel full of water weighed 512 grams, but afterwards it 
weighed only 357 grams. What was the specific gravity of 
the metal ? 

157. A piece of wood 1 m long, 30 cm wide, and 10 cm thick, 
is found to weigh 16.95 K . What is the specific gravity of the 
wood ? 

158. A granite obelisk 1 m square at the base, 60 cm square 
at the top, and 6 m high, terminates in a pyramid 30 cm high, 
making the total height of the obelisk 6.30 m . What is the 
weight of this obelisk in kilograms ? 



ANSWERS 



Ex. Ans. 


Ex. 


Ans. 


Ex. 


Ans. 


1. o.i™- 


53. 


44.478 A. 


105. 


77.2 k. 


2. 1.3 ™- 


54. 


2.04724 in. 


106. 


105.4 K - 


3. 21.4™ 


55. 


188.71376 lb. 


107. 


4,562 kilogram-meters 


4. 0.01™- 


56. 


6,340.08 gal. 


108. 


$1,440. 


5. 0.38 ™- 


■57. 


22.046 T. 


109. 


21™- 


6. 5.29™- 


58. 


40.2325 K ™ 


110. 


1,943.76 S( i-™- 


7. 0.001™- 


59. 


80.94 Ha - 


111. 


0.8494 S( i- ™- 


£. 0.048™ 


60. 


2, 265. 36 l 


112. 


742.9 sc i-™- 


9. 3.675™ 


61. 


15.087™- 


113. 


1,662.3 a - 


10. 4,250™- 


62. 


17.5065J 1 - 


114. 


4.8356 s <i- ™- 


11. 3,500™- 


63. 


618.9 e- 


115. 


1677 s< 5- dm - 


1#. 23,500™- 


64. 


88.9056 K %- 


116. 


1.20™- 


13. 9,460™- 


65. 


8.75 Km - 


117. 


5.64™- 


U. 9,240™- 


66. 


21.6 K ™- 


118. 


42.5 cm - 


15. 397™- 


67. 


39 Km - per hour. 


119. 


9.625 a - 


16. 720™- 


68. 


1.851 K ™-; 75 c ™ 


120. 


19.8 cu.m. 


17. 7.3™- 


69. 


47.5 Km - 


121. 


99.792 J - 


15. 50™- 


70. 


33 days 8 li. 


122. 


65.7 cm - 


19. 67.678™- 


71. 


3,245*6 sq. Kin. 


123. 


10.362 '• 


£0. 649.115™- 


72. 


$2,505.60. 


124- 


503.1. 


21. 415,990™ 


73. 


$745.20. 


125. 


399.3. 


22. 5.26749 K ™- 


74. 


16.8™- 


126. 


294.2. 


23. 35,000™- 


75. 


$367.50. 


127^ 


233.5. 


24. 86.62™- 


76. 


$163,800. 


128. 


185.3. 


25. 15,480™- 


77. 


0.063. 


129. 


136.6. 


26. 7l§™ 


78. 


0.625; 0.375. 


130. 


108.4. 


27. 73.50672 K ™ 


79. 


18,000. 


131. 


86.0. 133. 50.3. 


&9. 22.2075™ 


80. 


$10.89. 


132. 


63.4. 134. 39.9. 


29. 300 times. 


81. 


151.2 s - 


135. 


Dia. 108.4; dep. 216.7. 


50. 23.85 s< i-™ 


82. 


80. 


136. 


" 86.0; " 172.0 


51. 20 ™- 


83. 


0.869™- 


137. 


" 68.3; " 136.6. 


£0. $8.40. 


84. 


12/. 


138. 


" 50.3; " 100.6 


33. 217.5 ca -; 1.175 a - 


85. 


79|f days. 


139. 


" 39.9; " 79.9. 


&£. 4,585.76 a - 


86. 


2.88 T. 


140. 


" 31.7; " 63.4. 


35. $6,556.57. 


87. 


40,070.376 Km - 


Uh 


" 23.4; " 46.7. 


36. 12.043044049 cum - 


88. 


200. 


142. 


" 18.5; " 37.1. 


37. 153.41 cu -™ 


89. 


$11.04. 


143. 


12.528 K - 


38. $373. 72 J. 


90. 


$9. 


144- 


20.345 K - 


39. 369.6 loads. 


91. 


$1,338.62. 


145. 


13.3™™ 


40. $29.25. 


92. 


0.364 K - 


146. 


1,933.6 K - 


41. 12™-; $20.25. 


93. 


rim; 100. 


147. 


From 248 to 258 T. 


42. 20 f. 


94. 


32.5 L 


148. 


2.721 k. 


43. $1.23. 


95. 


10.61 DI < 


149. 


0.786 »■ 


4£ 75 1- 


96. 


80 K - 


150- 


169.07 K - 


45. 39 hl 


97. 


565 K - 


151. 


.5^1 cu. cm. . ^14 9_ 


^. 4.5™- 


98. 


20,202 sc i- K ™- 


152. 


0.8956, or about -ft. 


47. $3.09. 


99. 


14.2/. 


153. 


0.572. 


4?. $2.31. 


100. 


26.73 2- 


154. 


£ or 0.833. 


49. 135 grams. 


101. 


70.5/. 


155. 


1.093. 


50. 5.4 T. 


102. 


1.99/. 


156. 


9.24. 


51. 15,744 ft. 


103. 


34.83 H1 - 


157. 


0.565. 


51?. 31.0685 m. 


104. 


68.9 bu. 


158. 


From 10.48 to 10. 88 T. 






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